Normal form unique value

While there are infinitely many values of ai, a, and aj. which satisfy Eq. (4.28), the requirement that the wave function be normalized provides a final constraint in the form of Eq. (4.11). The unique values satisfying both equations are... 

A table is said to be in first normal form if each row has the same number of columns, each column has a value, and there are no duplicate rows. Because an RDBMS uses a table defined with a fixed number of columns, it is always true that each row contains the same number of columns. If one allows that null is a value, then every column will have a value. It should be obvious that repeating a row in a table is wasteful, but also potentially confusing and prone to error. For example, if two rows in a table of logP contained the same name and logP, one row may have the logP changed at some point. Then which row would be the correct row This condition also illustrates the final aspect of first normal form There should be at least one column, or combination of columns, that could function as a key that uniquely identifies the row. This is the name column or compound id column in the above examples. The data in this column must be unique. 

It is not required that such a column actually be used as an SQL key, but it is wise to do so. In this way, the SQL uniqueness constraints can help to ensure that the table is in first normal form. While this one column must be unique, it is entirely possible and even likely that some other data values will not be unique. For example, there are expected to be many compounds that coincidentally have the same logP. This does not violate first normal form. 

Another way to think about first normal form is to simply consider what the table is intended to contain. If it contains data about structures, then there must be a unique way to identify those structures, for example, by name. For a table that contains information about structures, it must contain only information about structures. It must contain simple values that are associated with that structure, for example, molecular weight or logP. It must not contain complex information about its data values, such as the method used to determine logP. 

First normal form Each table should contain only data about a unique entity. Each row should have a unique identifier. If data tables violate first normal form, a careful reconsideration of which information belongs in which table should be undertaken. A structure table should be about structures, a logP table about logP values, and a method table about methods. 

Equation (7-12) is a special case of the law of corresponding states which predicts that equations of state of all normal substances are the same, if the volume, pressure, and temperature are expressed in terms of their respective values for some unique point in the equation, such as the critical point. Any equation of state which contains two constants characteristic of the gas can be cast into such a form that the law of corresponding states applies. 

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